<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-03-01</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001819253</issuerCik>
        <issuerName>Haymaker Acquisition Corp. III</issuerName>
        <issuerTradingSymbol>HYACU</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001455717</rptOwnerCik>
            <rptOwnerName>Mayerson Frederic H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>501 MADISON AVENUE, FLOOR 12</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>The reporting person has an indirect pecuniary interest in shares of Class B common stock of the Issuer through his membership interest in Haymaker Sponsor III LLC, over which the reporting person does not have voting or dispositive control.</remarks>

    <ownerSignature>
        <signatureName>/s/ Frederic H. Mayerson</signatureName>
        <signatureDate>2021-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
